When an object is removed from a furnace and placed in an enviroment with a constant temperature of 90°F, its core temperature is 1500°F. Five hours later the core temperature is 390°F.

Explain why there must exist a time in the interval when the temperature is decreasing at rate of 222° degrees F per hour,

Question

When an object is removed from a furnace and placed in an enviroment with a constant temperature of 90°F, its core temperature is 1500°F. Five hours later the core temperature is 390°F.

Explain why there must exist a time in the interval when the temperature is decreasing at rate of 222° degrees F per hour,

anonymous · Answer

This is a perfect example of intermediate value theorem!

anonymous · Answer

I have no idea how to explain this with math but the rate of the decrease in temperature should be on exponential function from what I remember. It will decrease at 1500 much faster than it will at 500 hundred because the temperature difference is greater. the average rate is 390/5.